Finite Group Databasebeta

← #386355

Subgroups — #386355

Order 512.

1452 conjugacy classes of subgroups.

The subgroup lattice has 972 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#1895C211yesmaximal, characteristic
2#13973C211yesmaximal, characteristic, complemented
3#13970C211yesmaximal, characteristic
4#11315C211yesmaximal, characteristic, complemented
5#11315C211yesmaximal, characteristic, complemented
6#11293C211yesmaximal, characteristic, complemented
7#11199C211yesmaximal, characteristic, complemented
8#11066C211yesmaximal, characteristic, complemented
9#10969C211yesmaximal, characteristic
10#10931C211yesmaximal, characteristic, complemented
11#10807C211yesmaximal, characteristic, complemented
12#10788C211yesmaximal, characteristic, complemented
13#10788C211yesmaximal, characteristic, complemented
14#10722C211yesmaximal, characteristic, complemented
15#10715C211yesmaximal, characteristic, complemented
16C23×M16C2211yescharacteristic
17C22×#121C2211yescharacteristic
18C22×C4×D4C2211yescharacteristic
19C22×#102C2211yescharacteristic
20C22×#102C2211yescharacteristic
21C22×#102C2211yescharacteristic
22C22×#102C2211yescharacteristic
23C22×C22⋊C8C2211yescharacteristic
24C2×#390C2211yescharacteristic
25C2×#389C2211yescharacteristic
26C2×#386—21no—
27C2×#380C2211yescharacteristic
28C2×#380C2211yescharacteristic
29C2×#380C2211yescharacteristic
30C2×C4×C4⋊C4C2211yescharacteristic
31C2×C4×C22⋊C4C2211yescharacteristic
32#1895C418yescomplemented
33C2×#340C2211yescharacteristic
34C2×#340C2211yescharacteristic
35C2×#340C2211yescharacteristic
36C2×#340C2211yescharacteristic
37C2×#340C2211yescharacteristic
38C2×#340C2211yescharacteristic
39C2×#340C2211yescharacteristic
40C2×#340C2211yescharacteristic
41C2×#340C2211yescharacteristic
42C2×#340C2211yescharacteristic
43C2×#340C2211yescharacteristic
44C2×#340C2211yescharacteristic
45C2×#336C2211yescharacteristic
46C2×#336C2211yescharacteristic
47C2×#336C2211yescharacteristic
48C2×#336C2211yescharacteristic
49#1442—21no—
50#1440—21no—
51#1439—21no—
52#1438—21no—
53#1437—21no—
54C4⋊#95C2211yescharacteristic
55C4⋊#95C2211yescharacteristic
56C4⋊#95C2211yescharacteristic
57C4⋊#95C2211yescharacteristic
58#1434—21no—
59C22⋊#95—21no—
60C23×D4—21no—
61C23×D4C2311yescharacteristic
62C24×C4—21no—
63C24×C4C2311yescharacteristic
64C22×M16—41no—
65C22×M16—41no—
66C22×M16—41no—
67C22×M16—41no—
68C22×M16—41no—
69C22×M16—41no—
70C22×M16C2×C414yescomplemented
71C23×C8C2311yescharacteristic
72C23×C8C2311yescharacteristic
73C23×C8C2311yescharacteristic
74C23×C8C2311yescharacteristic
75C2×#121—22no—
76C2×#121—22no—
77C2×#121—22no—
78C2×#121—41no—
79C2×#121—41no—
80C2×#121C2×C414yes—
81C2×C4×D4—22no—
82C2×C4×D4—22no—
83C2×C4×D4—41no—
84C2×C4×D4—41no—
85C2×C4×D4—41no—
86C2×C4×D4—41no—
87C22×C4⋊C4—21no—
88C22×C4⋊C4C2311yescharacteristic
89C22×C4⋊C4C2311yescharacteristic
90C22×C4⋊C4C2311yescharacteristic
91C22×C4⋊C4C2311yescharacteristic
92C22×C4⋊C4C2311yescharacteristic
93C22×C4⋊C4C2311yescharacteristic
94C22×C4⋊C4C2311yescharacteristic
95C22×C22⋊C4—21no—
96C22×C22⋊C4—21no—
97C22×C22⋊C4—21no—
98C22×C22⋊C4—21no—
99C22×C22⋊C4—21no—
100C22×C22⋊C4—21no—
101C22×C22⋊C4—21no—
102C22×C22⋊C4D411yescharacteristic
103C22×C22⋊C4D411yescharacteristic
104C22×C42—21no—
105C22×C42C2311yescharacteristic
106C22×C42C2311yescharacteristic
107C2×#102—22no—
108C2×#102—22no—
109C2×#102—22no—
110C2×#102—41no—
111C2×#102—41no—
112C2×#102—41no—
113C2×#102—41no—
114C2×#102—41no—
115C2×#102—41no—
116C2×#102—41no—
117C2×#102C2×C414yes—
118C2×#102C2×C414yes—
119C2×C22⋊C8—22no—
120C2×C22⋊C8—41no—
121C2×C22⋊C8—41no—
122#390—22no—
123#390—41no—
124#389—41no—
125#389—41no—
126#386—44no—
127#380—22no—
128#380—22no—
129#380—22no—
130#380—41no—
131#380—41no—
132#380C2×C414yescomplemented
133C4×C4⋊C4—22no—
134C4×C4⋊C4—41no—
135C4×C22⋊C4—41no—
136C4×C22⋊C4—41no—
137C2×#95—21no—
138C2×#95—21no—
139C2×#95—21no—
140C2×#95—21no—
141C2×#95—21no—
142C2×#95—21no—
143C2×#95—21no—
144C2×#95—21no—
145C2×#95—21no—
146C2×#95—21no—
147C2×#95—21no—
148C2×#95—21no—
149C2×#95—21no—
150C2×#95D411yescharacteristic
151C2×#95D411yescharacteristic
152#340—22no—
153#340—41no—
154#340—41no—
155#340—41no—
156#340—41no—
157#340—41no—
158#340—41no—
159#340—41no—
160#340—41no—
161#340—41no—
162#340C2×C414yescomplemented
163#340C2×C414yescomplemented
164#336—41no—
165#336—41no—
166#336—41no—
167#336—41no—
168C25—21no—
169C25C2×D411yescharacteristic
170C22×D4—24no—
171C22×D4—21no—
172C22×D4—21no—
173C22×D4—21no—
174C22×D4—21no—
175C22×D4—21no—
176C22×D4—21no—
177C22×D4—21no—
178C22×D4—21no—
179C22×D4—21no—
180C22×D4—21no—
181C22×D4—21no—
182C22×D4—42no—
183C22×D4—42no—
184C22×D4—42no—
185C22×D4—42no—
186C22×D4—81no—
187C22×D4—81no—
188C22×D4C22×C412yes—
189C22×D4#4112yes—
190C22×D4#4112yes—
191C23×C4—21no—
192C23×C4—21no—
193C23×C4—21no—
194C23×C4—21no—
195C23×C4—21no—
196C23×C4—21no—
197C23×C4—21no—
198C23×C4—21no—
199C23×C4—21no—
200C23×C4—21no—
201C23×C4—21no—
202C23×C4—21no—
203C23×C4—21no—
204C23×C4—21no—
205C23×C4—21no—
206C23×C4—21no—
207C23×C4—21no—
208C23×C4—21no—
209C23×C4—21no—
210C23×C4—42no—
211C23×C4—42no—
212C23×C4—42no—
213C23×C4—42no—
214C23×C4—42no—
215C23×C4—81no—
216C23×C4—81no—
217C23×C4C22×C412yes—
218C23×C4C2×D411yescharacteristic
219C23×C4C2×D411yescharacteristic
220C23×C4C2×D411yescharacteristic
221C23×C4C2×D411yescharacteristic
222C23×C4C2×D411yescharacteristic
223C23×C4#4112yes—
224C23×C4C2411yescharacteristic
225C2×M16—44no—
226C2×M16—44no—
227C2×M16—44no—
228C2×M16—44no—
229C2×M16—44no—
230C2×M16—44no—
231C2×M16—44no—
232C22×C8—21no—
233C22×C8—21no—
234C22×C8—21no—
235C22×C8—21no—
236C22×C8—21no—
237C22×C8—21no—
238C22×C8—21no—
239C22×C8—21no—
240C22×C8—21no—
241C22×C8—21no—
242C22×C8—21no—
243C22×C8—21no—
244C22×C8—21no—
245C22×C8—21no—
246C22×C8—21no—
247C22×C8—21no—
248C22×C8—21no—
249C22×C8—21no—
250C22×C8—21no—
251C22×C8—21no—
252C22×C8—21no—
253C22×C8—21no—
254C22×C8—21no—
255C22×C8—21no—
256C22×C8—21no—
257C22×C8—21no—
258C22×C8C22×C412yes—
259C22×C8C22×C412yes—
260#121—28no—
261#121—44no—
262#121—44no—
263#121—44no—
264C4×D4—44no—
265C4×D4—44no—
266C4×D4—44no—
267C4×D4—44no—
268C2×C4⋊C4—21no—
269C2×C4⋊C4—21no—
270C2×C4⋊C4—21no—
271C2×C4⋊C4—21no—
272C2×C4⋊C4—21no—
273C2×C4⋊C4—21no—
274C2×C4⋊C4—21no—
275C2×C4⋊C4—21no—
276C2×C4⋊C4—21no—
277C2×C4⋊C4—21no—
278C2×C4⋊C4—21no—
279C2×C4⋊C4—21no—
280C2×C4⋊C4—21no—
281C2×C4⋊C4—21no—
282C2×C4⋊C4—21no—
283C2×C4⋊C4—21no—
284C2×C4⋊C4—21no—
285C2×C4⋊C4—21no—
286C2×C4⋊C4—21no—
287C2×C4⋊C4—21no—
288C2×C4⋊C4—21no—
289C2×C4⋊C4—21no—
290C2×C4⋊C4—21no—
291C2×C4⋊C4—21no—
292C2×C4⋊C4—21no—
293C2×C4⋊C4—21no—
294C2×C4⋊C4—21no—
295C2×C4⋊C4—21no—
296C2×C4⋊C4—21no—
297C2×C4⋊C4—21no—
298C2×C4⋊C4—21no—
299C2×C4⋊C4—21no—
300C2×C4⋊C4—21no—
301C2×C4⋊C4—21no—
302C2×C4⋊C4—21no—
303C2×C4⋊C4—21no—
304C2×C4⋊C4—21no—
305C2×C4⋊C4—42no—
306C2×C4⋊C4—81no—
307C2×C4⋊C4—81no—
308C2×C4⋊C4C22×C412yes—
309C2×C4⋊C4C22×C412yes—
310C2×C4⋊C4C22×C412yes—
311C2×C4⋊C4#4112yes—
312C2×C4⋊C4#4112yes—
313C2×C22⋊C4—24no—
314C2×C22⋊C4—22no—
315C2×C22⋊C4—22no—
316C2×C22⋊C4—24no—
317C2×C22⋊C4—41no—
318C2×C22⋊C4—41no—
319C2×C22⋊C4—41no—
320C2×C22⋊C4—41no—
321C2×C22⋊C4—42no—
322C2×C22⋊C4—42no—
323C2×C22⋊C4—42no—
324C2×C22⋊C4—42no—
325C2×C22⋊C4—42no—
326C2×C22⋊C4—42no—
327C2×C22⋊C4—42no—
328C2×C22⋊C4—42no—
329C2×C22⋊C4—42no—
330C2×C22⋊C4—42no—
331C2×C22⋊C4—42no—
332C2×C22⋊C4—42no—
333C2×C22⋊C4—42no—
334C2×C22⋊C4—81no—
335C2×C22⋊C4—81no—
336C2×C22⋊C4—81no—
337C2×C22⋊C4—81no—
338C2×C22⋊C4—81no—
339C2×C22⋊C4—81no—
340C2×C42—21no—
341C2×C42—21no—
342C2×C42—21no—
343C2×C42—21no—
344C2×C42—21no—
345C2×C42—21no—
346C2×C42—21no—
347C2×C42—21no—
348C2×C42—21no—
349C2×C42—21no—
350C2×C42—21no—
351C2×C42—21no—
352C2×C42—42no—
353C2×C42—42no—
354C2×C42—81no—
355#102—44no—
356#102—44no—
357#102—44no—
358#102—44no—
359C22⋊C8—44no—
360#95—24no—
361#95—41no—
362#95—41no—
363#95—42no—
364#95—42no—
365#95—42no—
366#95—42no—
367#95—42no—
368#95—42no—
369#95—42no—
370#95—81no—
371#95—81no—
372#95—81no—
373#95—81no—
374#95—81no—
375C24—22no—
376C24—21no—
377C24—21no—
378C24—22no—
379C24—21no—
380C24—21no—
381C24—22no—
382C24—21no—
383C24—21no—
384C24—21no—
385C24—21no—
386C24—21no—
387C24—21no—
388C24—21no—
389C24—21no—
390C24—21no—
391C24—21no—
392C24—41no—
393C24—41no—
394C24—41no—
395C24—41no—
396C24—41no—
397C24—41no—
398C24—41no—
399C24—41no—
400C24—41no—
401C24—41no—
402C24—41no—
403C24—41no—
404C24C4×D412yes—
405C24C22×D411yescharacteristic
406C2×D4—22no—
407C2×D4—22no—
408C2×D4—22no—
409C2×D4—22no—
410C2×D4—22no—
411C2×D4—22no—
412C2×D4—22no—
413C2×D4—22no—
414C2×D4—22no—
415C2×D4—22no—
416C2×D4—22no—
417C2×D4—22no—
418C2×D4—22no—
419C2×D4—22no—
420C2×D4—22no—
421C2×D4—48no—
422C2×D4—48no—
423C2×D4—41no—
424C2×D4—41no—
425C2×D4—41no—
426C2×D4—41no—
427C2×D4—41no—
428C2×D4—41no—
429C2×D4—41no—
430C2×D4—41no—
431C2×D4—41no—
432C2×D4—41no—
433C2×D4—41no—
434C2×D4—41no—
435C2×D4—84no—
436C2×D4—84no—
437C2×D4—84no—
438C2×D4—84no—
439C2×D4—84no—
440C2×D4#11714yes—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—41no—
491C22×C4—41no—
492C22×C4—41no—
493C22×C4—41no—
494C22×C4—41no—
495C22×C4—41no—
496C22×C4—41no—
497C22×C4—41no—
498C22×C4—41no—
499C22×C4—41no—
500C22×C4—41no—
501C22×C4—41no—
502C22×C4—41no—
503C22×C4—41no—
504C22×C4—41no—
505C22×C4—41no—
506C22×C4—48no—
507C22×C4—41no—
508C22×C4—41no—
509C22×C4—41no—
510C22×C4—41no—
511C22×C4—41no—
512C22×C4—41no—
513C22×C4—41no—
514C22×C4—41no—
515C22×C4—41no—
516C22×C4—41no—
517C22×C4—41no—
518C22×C4—41no—
519C22×C4—41no—
520C22×C4—41no—
521C22×C4—41no—
522C22×C4—41no—
523C22×C4—41no—
524C22×C4—41no—
525C22×C4—41no—
526C22×C4—41no—
527C22×C4—41no—
528C22×C4—41no—
529C22×C4—41no—
530C22×C4—41no—
531C22×C4—41no—
532C22×C4—41no—
533C22×C4—41no—
534C22×C4—41no—
535C22×C4—41no—
536C22×C4—41no—
537C22×C4—41no—
538C22×C4—41no—
539C22×C4—41no—
540C22×C4—41no—
541C22×C4—41no—
542C22×C4—41no—
543C22×C4—41no—
544C22×C4—41no—
545C22×C4—41no—
546C22×C4—41no—
547C22×C4—41no—
548C22×C4—41no—
549C22×C4—41no—
550C22×C4—41no—
551C22×C4—84no—
552C22×C4—84no—
553C22×C4—84no—
554C22×C4—84no—
555C22×C4—84no—
556C22×C4—84no—
557C22×C4C4×D412yes—
558C22×C4AGL(1,ℤ/8)12yes—
559C22×C4#13712yes—
560C22×C4C23×C411yescharacteristic
561C22×C4C2×#4111yescharacteristic
562C22×C4C2×#4111yescharacteristic
563C22×C4C2×#4111yescharacteristic
564C22×C4C2×#4111yescharacteristic
565C22×C4C2×#4111yescharacteristic
566C22×C4H(5,𝔽2)11yescharacteristic
567C22×C4H(5,𝔽2)11yescharacteristic
568C22×C4H(5,𝔽2)11yescharacteristic
569C22×C4H(5,𝔽2)11yescharacteristic
570C22×C4H(5,𝔽2)11yescharacteristic
571C22×C4H(5,𝔽2)11yescharacteristic
572C22×C4H(5,𝔽2)11yescharacteristic
573C22×C42−1+411yescharacteristic
574M16—416no—
575C2×C8—22no—
576C2×C8—22no—
577C2×C8—22no—
578C2×C8—22no—
579C2×C8—22no—
580C2×C8—22no—
581C2×C8—41no—
582C2×C8—41no—
583C2×C8—41no—
584C2×C8—41no—
585C2×C8—41no—
586C2×C8—41no—
587C2×C8—41no—
588C2×C8—41no—
589C2×C8—41no—
590C2×C8—41no—
591C2×C8—41no—
592C2×C8—41no—
593C2×C8—41no—
594C2×C8—41no—
595C2×C8—41no—
596C2×C8—41no—
597C2×C8—41no—
598C2×C8—41no—
599C2×C8—41no—
600C2×C8—41no—
601C2×C8—41no—
602C2×C8—41no—
603C4⋊C4—22no—
604C4⋊C4—22no—
605C4⋊C4—22no—
606C4⋊C4—22no—
607C4⋊C4—22no—
608C4⋊C4—22no—
609C4⋊C4—22no—
610C4⋊C4—22no—
611C4⋊C4—22no—
612C4⋊C4—22no—
613C4⋊C4—41no—
614C4⋊C4—41no—
615C4⋊C4—41no—
616C4⋊C4—41no—
617C4⋊C4—41no—
618C4⋊C4—41no—
619C4⋊C4—41no—
620C4⋊C4—41no—
621C4⋊C4—41no—
622C4⋊C4—41no—
623C4⋊C4—41no—
624C4⋊C4—41no—
625C4⋊C4—41no—
626C4⋊C4—41no—
627C4⋊C4—41no—
628C4⋊C4—41no—
629C4⋊C4—41no—
630C4⋊C4—41no—
631C4⋊C4—84no—
632C22⋊C4—48no—
633C22⋊C4—44no—
634C22⋊C4—44no—
635C22⋊C4—48no—
636C22⋊C4—84no—
637C22⋊C4—84no—
638C22⋊C4—84no—
639C22⋊C4—84no—
640C22⋊C4—84no—
641C42—41no—
642C42—41no—
643C42—41no—
644C42—41no—
645C42—41no—
646C42—41no—
647C42—41no—
648C42—41no—
649C42—84no—
650C23—22no—
651C23—24no—
652C23—22no—
653C23—22no—
654C23—22no—
655C23—22no—
656C23—22no—
657C23—22no—
658C23—41no—
659C23—42no—
660C23—41no—
661C23—41no—
662C23—42no—
663C23—42no—
664C23—41no—
665C23—42no—
666C23—41no—
667C23—41no—
668C23—41no—
669C23—41no—
670C23—41no—
671C23—42no—
672C23—42no—
673C23—42no—
674C23—42no—
675C23—42no—
676C23—41no—
677C23—42no—
678C23—41no—
679C23—42no—
680C23—41no—
681C23—41no—
682C23—41no—
683C23—41no—
684C23—41no—
685C23—42no—
686C23—42no—
687C23—41no—
688C23—42no—
689C23—41no—
690C23—41no—
691C23—41no—
692C23—41no—
693C23—42no—
694C23—41no—
695C23—41no—
696C23—42no—
697C23—41no—
698C23—41no—
699C23—41no—
700C23—42no—
701C23—41no—
702C23—42no—
703C23—41no—
704C23—81no—
705C23—81no—
706C23—81no—
707C23—81no—
708C23—81no—
709C23—81no—
710C23—81no—
711C23—81no—
712C23—81no—
713C23—81no—
714C23—81no—
715C23—81no—
716C23—81no—
717C23—81no—
718C23—81no—
719C23—81no—
720C23C2×C4×D411yescharacteristic
721C23#53411yescharacteristic
722C23#53711yescharacteristic
723C23#54611yescharacteristic
724C23#54611yescharacteristic
725C23#54611yescharacteristic
726C23#54611yescharacteristic
727C23C2×AGL(1,ℤ/8)11yescharacteristic
728C23C2×#13711yescharacteristic
729C23#57511yescharacteristic
730C23#57511yescharacteristic
731C23#57611yescharacteristic
732C23#57611yescharacteristic
733C23#57711yescharacteristic
734C23#57711yescharacteristic
735D4—24no—
736D4—24no—
737D4—42no—
738D4—42no—
739D4—42no—
740D4—42no—
741D4—42no—
742D4—42no—
743D4—816no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—41no—
754C2×C4—41no—
755C2×C4—41no—
756C2×C4—41no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4—41no—
762C2×C4—41no—
763C2×C4—41no—
764C2×C4—41no—
765C2×C4—42no—
766C2×C4—42no—
767C2×C4—42no—
768C2×C4—42no—
769C2×C4—42no—
770C2×C4—42no—
771C2×C4—42no—
772C2×C4—42no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—42no—
777C2×C4—42no—
778C2×C4—42no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—42no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—42no—
787C2×C4—42no—
788C2×C4—42no—
789C2×C4—42no—
790C2×C4—42no—
791C2×C4—42no—
792C2×C4—42no—
793C2×C4—41no—
794C2×C4—42no—
795C2×C4—42no—
796C2×C4—41no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—42no—
800C2×C4—42no—
801C2×C4—41no—
802C2×C4—816no—
803C2×C4—81no—
804C2×C4—81no—
805C2×C4—81no—
806C2×C4—81no—
807C2×C4—81no—
808C2×C4—81no—
809C2×C4—81no—
810C2×C4—81no—
811C2×C4—81no—
812C2×C4—81no—
813C2×C4—81no—
814C2×C4—81no—
815C2×C4—81no—
816C2×C4—81no—
817C2×C4—81no—
818C2×C4—81no—
819C2×C4—81no—
820C2×C4—81no—
821C2×C4—81no—
822C2×C4—81no—
823C2×C4—81no—
824C2×C4—81no—
825C2×C4—81no—
826C2×C4—81no—
827C2×C4—81no—
828C2×C4—81no—
829C2×C4—81no—
830C2×C4—81no—
831C2×C4—81no—
832C2×C4—81no—
833C2×C4—81no—
834C2×C4—81no—
835C2×C4—81no—
836C2×C4—81no—
837C2×C4C2×#11711yescharacteristic
838C2×C4C4×#4111yescharacteristic
839C2×C4#51811yescharacteristic
840C2×C4#51811yescharacteristic
841C2×C4#51811yescharacteristic
842C2×C4#52011yescharacteristic
843C2×C4#53811yescharacteristic
844C2×C4#53811yescharacteristic
845C2×C4#53811yescharacteristic
846C2×C4#53811yescharacteristic
847C2×C4#53911yescharacteristic
848C2×C4#53911yescharacteristic
849C2×C4#53911yescharacteristic
850C2×C4#53911yescharacteristic
851C2×C4#54011yescharacteristic
852C2×C4#54211yescharacteristic
853C2×C4#55111yescharacteristic
854C2×C4#55111yescharacteristic
855C2×C4#55111yescharacteristic
856C2×C4#55111yescharacteristic
857C2×C4#55311yescharacteristic
858C2×C4#55311yescharacteristic
859C2×C4#55311yescharacteristic
860C2×C4#55311yescharacteristic
861C2×C4#56011yescharacteristic
862C2×C4#56011yescharacteristic
863C2×C4#56011yescharacteristic
864C2×C4H(3,𝔽4)11yescharacteristic
865C8—42no—
866C8—42no—
867C8—81no—
868C8—81no—
869C22—42no—
870C22—44no—
871C22—42no—
872C22—44no—
873C22—42no—
874C22—44no—
875C22—42no—
876C22—42no—
877C22—42no—
878C22—42no—
879C22—81no—
880C22—82no—
881C22—81no—
882C22—82no—
883C22—82no—
884C22—81no—
885C22—81no—
886C22—82no—
887C22—81no—
888C22—82no—
889C22—81no—
890C22—82no—
891C22—82no—
892C22—82no—
893C22—82no—
894C22—81no—
895C22—82no—
896C22—81no—
897C22—82no—
898C22—82no—
899C22#232511yescharacteristic
900C22#234211yescharacteristic
901C22#236411yescharacteristic
902C22#268411yescharacteristic
903C22#268811yescharacteristic
904C22#269111yescharacteristic
905C22#269311yescharacteristic
906C22C4×AGL(1,ℤ/8)11yescharacteristic
907C22C4×#13711yescharacteristic
908C22#294611yescharacteristic
909C22#294611yescharacteristic
910C22#319411yescharacteristic
911C22#319611yescharacteristic
912C22#319811yescharacteristic
913C22#319811yescharacteristic
914C22#325411yescharacteristic
915C22#325611yescharacteristic
916C22#325911yescharacteristic
917C22#326311yescharacteristic
918C22#330711yescharacteristic
919C22#331011yescharacteristic
920C22#331411yescharacteristic
921C22#331811yescharacteristic
922C22#331911yescharacteristic
923C22#331911yescharacteristic
924C22#332011yescharacteristic
925C22#332111yescharacteristic
926C22#332211yescharacteristic
927C22#332211yescharacteristic
928C22#332311yescharacteristic
929C22#332311yescharacteristic
930C22#332511yescharacteristic
931C22#333111yescharacteristic
932C22#333211yescharacteristic
933C22#333311yescharacteristic
934C4—42no—
935C4—42no—
936C4—42no—
937C4—82no—
938C4—81no—
939C4—82no—
940C4—82no—
941C4—82no—
942C4—81no—
943C4—82no—
944C4—161no—
945C4—161no—
946C4#231811yescharacteristic
947C4#233511yescharacteristic
948C4#235311yescharacteristic
949C4#237511yescharacteristic
950C4#274611yescharacteristic
951C4#274911yescharacteristic
952C4#277811yescharacteristic
953C4#278211yescharacteristic
954C2—82no—
955C2—84no—
956C2#1442711yescharacteristic
957C2#2219111yescharacteristic
958C2#2219911yescharacteristic
959C2#2257811yescharacteristic
960C2#2258411yescharacteristic
961C2#2314011yescharacteristic
962C2#2314211yescharacteristic
963C2#3127611yescharacteristic
964C2#3127911yescharacteristic
965C2#3140811yescharacteristic
966C2#3141311yescharacteristic
967C2#3151011yescharacteristic
968C2#3151511yescharacteristic
969C2#3156611yescharacteristic
970C2#3156911yescharacteristic
subgroupG/H
center, socleC24C22×D4
commutatorC22×C4C23×C4
Frattini, cosocleC23×C4C24
prime radicalC22×#121C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C2×C4×C22⋊C4 ◁ G
LECSG ▷ C23×C4 ▷ C2 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. #13973C2semidirect
4. #11315C2semidirect
5. #11315C2semidirect
6. #11293C2semidirect
7. #11199C2semidirect
8. #11066C2semidirect
10. #10931C2semidirect
11. #10807C2semidirect
12. #10788C2semidirect
13. #10788C2semidirect
14. #10722C2semidirect
15. #10715C2semidirect
32. #1895C4semidirect
70. C22×M16C2×C4semidirect
132. #380C2×C4semidirect
162. #340C2×C4semidirect
163. #340C2×C4semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#18952
#139732
#139702
#113152
#112932
#111992
#110662
#109692
#109312
#108072
#107882
#107222
#107152